CN108732932B - Four-rotor unmanned aerial vehicle accurate position control method based on minimum variance regulator - Google Patents

Four-rotor unmanned aerial vehicle accurate position control method based on minimum variance regulator Download PDF

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CN108732932B
CN108732932B CN201810555651.5A CN201810555651A CN108732932B CN 108732932 B CN108732932 B CN 108732932B CN 201810555651 A CN201810555651 A CN 201810555651A CN 108732932 B CN108732932 B CN 108732932B
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position control
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unmanned aerial
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CN108732932A (en
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于洋
施泽楠
张鑫
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Hetang Intelligent Technology Gu'an Co ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/04—Control of altitude or depth
    • G05D1/042—Control of altitude or depth specially adapted for aircraft
    • G05D1/046—Control of altitude or depth specially adapted for aircraft to counteract a perturbation, e.g. gust of wind

Abstract

The invention discloses a precise position control method of a quad-rotor unmanned aerial vehicle based on a minimum variance regulator, which comprises the following two parts: identifying a position control model of the quad-rotor unmanned aerial vehicle and designing a position control minimum variance regulator, wherein the position control model identification is mainly used for obtaining an unmanned aerial vehicle position control ARMA model containing noise description by an augmented least square method; the design of the minimum variance regulator is mainly aiming at the ARMA model obtained in the prior art, and the influence of noise on the control precision is minimized through the estimation and compensation of the noise. The method can effectively improve the position control precision of the quad-rotor unmanned aerial vehicle during suspension, and can effectively reduce the influence of system noise on the position control precision during suspension, thereby realizing high-precision position control.

Description

Four-rotor unmanned aerial vehicle accurate position control method based on minimum variance regulator
Technical Field
The invention relates to a method for controlling the accurate position of a quad-rotor unmanned aerial vehicle, in particular to a method for controlling the accurate position of the quad-rotor unmanned aerial vehicle based on a minimum variance regulator, and belongs to the technical field of unmanned aerial vehicle flight control application.
Background
In recent years, with the development of new materials, micro-electromechanical systems, power electronics, and microprocessor technologies, quad-rotor aircraft have been rapidly developed. The system is suitable for performing tasks such as monitoring and reconnaissance in a near-ground and complex environment, and has wide military and civil prospects; the unique flight control mode attracts a large number of students to research.
In the field of quad rotor control, the GRASP laboratory at pennsylvania university is in the world's lead. Their quadrotors have been able to perform complex maneuvers indoors, such as through a narrow inclined window, turning 720 degrees in the air, hanging upside down on an inclined wall, etc. In addition, the research of the aircraft on formation flying is also well established, so that the aircraft can fly around the 8 shape and can also pass through narrow passages. Many colleges and universities in China research the control of the four rotors, but the research level is backward on the whole, and most of the research level still stays in the theoretical and simulation stages. Although researchers have also proposed various algorithms such as PID, H ∞, Backstepping, sliding mode control, etc., few algorithms are added to practical systems for validation. In addition, in view of the situations at home and abroad, the research in the current four-rotor control field mainly focuses on the large maneuvering, robust and formation control of the four rotors, and few researches are related to the improvement of the control precision of the four rotors during suspension. However, high-precision hovering position control is necessary for practical applications such as aerial photography and cargo delivery. The influence of system noise on the position control precision is large during suspension, so that the method for controlling the precise position of the quad-rotor unmanned aerial vehicle based on the minimum variance regulator is provided for solving the problems.
Disclosure of Invention
The invention aims to solve the problems and provide a method for controlling the precise position of a quadrotor unmanned aerial vehicle based on a minimum variance regulator, which can effectively reduce the influence of system noise on the position control precision during hovering, thereby realizing high-precision position control.
The invention realizes the aim through the following technical scheme, and the method for controlling the accurate position of the quadrotor unmanned aerial vehicle based on the minimum variance regulator is characterized in that a small quadrotor unmanned aerial vehicle is used as a controlled object, an ARMA (autoregressive moving average) model for controlling the position of the quadrotor unmanned aerial vehicle is obtained through system identification, and then a minimum variance controller is designed for the quadrotor unmanned aerial vehicle, so that the accurate hovering position control of the quadrotor unmanned aerial vehicle is realized; an ARMA model for unmanned aerial vehicle position control is obtained through an augmented least square method, and then a minimum variance controller is designed aiming at the ARMA model, wherein the control method comprises the following steps:
step A, designing a position control PD controller, wherein the attitude angle of the PD controller is generally expressed by using a Z-Y-X Euler angle and is named as a yaw angle, a pitch angle and a roll angle respectively, the position control in the Z direction of four rotors uses the lift sum change of four propellers as input quantity, the position in the X direction uses the pitch angle as input quantity, and the position in the Y direction uses the roll angle as input quantity; because the attitude angle and the horizontal acceleration are approximately in a positive ratio under a small angle, a transfer function from the pitch angle to the position in the X direction is approximately a second-order integral link; the lift force of the motor is in direct proportion to the vertical acceleration, and a second-order integral link is used for expressing a transfer function from the lift force to the height; the position control transfer functions in three directions are unstable under the open loop condition; the minimum variance regulator requires the controlled object to be stable; therefore, firstly, a position closed loop is required to be designed to enable position control to be a stable system, and controllers are respectively designed for three axial positions by adopting a PD-based method;
the pitch to X-axis position transfer function is:
Figure BDA0001682317800000021
wherein g is the gravity acceleration, theta is the pitch angle, and X is the position in the X direction;
selecting a PD controller as follows:
Figure BDA0001682317800000022
wherein theta iscFor pitch angle command, xcFor position commands, KPAnd KDRespectively a proportional parameter and a differential parameter of the controller;
in addition, the closed loop of the pitch angle can be approximated as a link, namely:
Figure BDA0001682317800000023
the transfer function of the position closed loop thus obtained is:
Figure BDA0001682317800000031
and B, selecting a position closed loop ARMA model, wherein in order to realize a computer program, a discrete model is selected to model each axis of the four-rotor position control, in addition, the model also comprises description about noise so as to compensate the noise in subsequent control, and a third-order ARMA model is selected to describe the position control of the four rotors in a single axial direction:
Figure BDA0001682317800000032
wherein xc(k) Inputting a position instruction at the time k; x (k) is the position response output at time k; v (k) is the noise at time k; q. q.s-iDelaying by i cycles for the delay factor representation, i.e. x (k-i) ═ q-ix (k) v (k); is that the variance is sigma2The white noise sequence of (a);
step C, identifying position closed loop ARMA model parameters: adding a pseudo-random position instruction sequence with proper amplitude to an aircraft with a position closed loop during identification; selecting 4-order M sequence as random input xc(k) K is 0, 1, 2, the amplitude is 0.5m, and the period is 100 ms; obtaining a position response sequence x (k) of the quad-rotor unmanned aerial vehicle through an actual flight test, wherein k is 0, 1, 2;
order to
Figure BDA0001682317800000033
According to formula (5) have
x(k)＝hT(k)θ+v(k) (7)
Further, the estimated value of the model parameter θ can be obtained by the following augmented least squares recursive algorithm
Figure BDA0001682317800000034
Figure BDA0001682317800000041
The variable k represents the kth iteration;
Figure BDA0001682317800000042
giving a group of approximately accurate values according to experience, and setting P (0) as a unit matrix large enough; when in use
Figure BDA0001682317800000043
The iteration can be stopped when the change is small along with the increase of the iteration times; finally, a set of estimated values of the model parameters is obtained,
Figure BDA0001682317800000044
step C, designing a position closed loop minimum variance regulator: minimum variance regulator designed according to
Figure BDA0001682317800000045
The minimum variance regulator is added to the system as an outer loop of the position closed loop;
bringing formula (9) into formula (5)
Figure BDA0001682317800000046
Bringing formula (9) and formula (10) into formula (5)
Figure BDA0001682317800000047
It can be seen that there are times when the parameter estimate is equal to the true value
x(k)＝v(k) (12)
At this time, the controlled quantity x (k) reaches a minimum variance, i.e.
E{[x(k)]2}＝σ2 (13)
Preferably, the control different from the horizontal position in step B takes the posture as an inner ring, the height is described by using a second-order ARMA model because a motor rotating speed instruction is directly used as a control input, the time constant of the motor is small, and the dynamic characteristic of the inner ring is not considered in the height channel.
The invention has the beneficial effects that: according to the invention, through the design of the position control model identification and the position control minimum variance regulator of the quad-rotor unmanned aerial vehicle, the position control model identification mainly obtains an unmanned aerial vehicle position control ARMA model containing noise description through an augmented least square method; the minimum variance regulator is designed mainly aiming at the ARMA model obtained in the front, and the influence of noise on the control precision is minimized through the estimation and compensation of the noise.
Drawings
Figure 1 is a block diagram of a quad-rotor drone of the present invention;
fig. 2 is a block diagram of a quad-rotor drone position control minimum variance regulator of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-2, a method for controlling the precise position of a quad-rotor unmanned aerial vehicle based on a minimum variance regulator is disclosed, in which a small quad-rotor unmanned aerial vehicle is used as a controlled object, an ARMA model for controlling the position of the quad-rotor unmanned aerial vehicle is obtained through system identification, and a minimum variance controller is designed for the quad-rotor unmanned aerial vehicle, so as to realize the precise suspension position control of the quad-rotor unmanned aerial vehicle; an ARMA model for unmanned aerial vehicle position control is obtained through an augmented least square method, and then a minimum variance controller is designed aiming at the ARMA model, wherein the control method comprises the following steps:
step A, designing a position control PD controller, wherein the attitude angle of the PD controller is generally expressed by using a Z-Y-X Euler angle and is named as a yaw angle, a pitch angle and a roll angle respectively, the position control in the Z direction of four rotors uses the lift sum change of four propellers as input quantity, the position in the X direction uses the pitch angle as input quantity, and the position in the Y direction uses the roll angle as input quantity; because the attitude angle and the horizontal acceleration are approximately in a positive ratio under a small angle, a transfer function from the pitch angle to the position in the X direction is approximately a second-order integral link; the lift force of the motor is in direct proportion to the vertical acceleration, and a second-order integral link is used for expressing a transfer function from the lift force to the height; the position control transfer functions in three directions are unstable under the open loop condition; the minimum variance regulator requires the controlled object to be stable; therefore, firstly, a position closed loop is required to be designed to enable position control to be a stable system, and controllers are respectively designed for three axial positions by adopting a PD-based method;
the pitch to X-axis position transfer function is:
Figure BDA0001682317800000061
wherein g is the gravity acceleration, theta is the pitch angle, and X is the position in the X direction;
selecting a PD controller as follows:
Figure BDA0001682317800000062
wherein theta iscFor pitch angle command, xcFor position commands, KPAnd KDRespectively a proportional parameter and a differential parameter of the controller;
in addition, the closed loop of the pitch angle can be approximated as a link, namely:
Figure BDA0001682317800000063
the transfer function of the position closed loop thus obtained is:
Figure BDA0001682317800000064
and B, selecting a position closed loop ARMA model, wherein in order to realize a computer program, a discrete model is selected to model each axis of the four-rotor position control, in addition, the model also comprises description about noise so as to compensate the noise in subsequent control, and a third-order ARMA model is selected to describe the position control of the four rotors in a single axial direction:
Figure BDA0001682317800000065
wherein xc(k) Inputting a position instruction at the time k; x (k) is the position response output at time k; v (k) is the noise at time k; q. q.s-iDelaying by i cycles for the delay factor representation, i.e. x (k-i) ═ q-ix (k) v (k); is that the variance is sigma2The white noise sequence of (a);
step C, identifying position closed loop ARMA model parameters: adding a pseudo-random position instruction sequence with proper amplitude to an aircraft with a position closed loop during identification; selecting 4-order M sequence as random input xc(k) K is 0, 1, 2, the amplitude is 0.5m, and the period is 100 ms; obtaining a position response sequence x (k) of the quad-rotor unmanned aerial vehicle through an actual flight test, wherein k is 0, 1, 2;
order to
Figure BDA0001682317800000071
According to formula (5) have
x(k)＝hT(k)θ+v(k) (7)
Further, the model parameter θ can be obtained by the following augmented least squares recursion algorithmEstimated value
Figure BDA0001682317800000072
Figure BDA0001682317800000073
The variable k represents the kth iteration;
Figure BDA0001682317800000074
giving a group of approximately accurate values according to experience, and setting P (0) as a unit matrix large enough; when in use
Figure BDA0001682317800000075
The iteration can be stopped when the change is small along with the increase of the iteration times; finally, a set of estimated values of the model parameters is obtained,
Figure BDA0001682317800000076
step C, designing a position closed loop minimum variance regulator: minimum variance regulator designed according to
Figure BDA0001682317800000077
The minimum variance regulator is added to the system as an outer loop of the position closed loop;
bringing formula (9) into formula (5)
Figure BDA0001682317800000078
Bringing formula (9) and formula (10) into formula (5)
Figure BDA0001682317800000079
It can be seen that there are times when the parameter estimate is equal to the true value
x(k)＝v(k) (12)
At this time, the controlled quantity x (k) reaches a minimum variance, i.e.
E{[x(k)]2}＝σ2 (13)
In the step B, the attitude is used as an inner ring different from the horizontal position control, the height directly uses a motor rotating speed instruction as a control input, the time constant of the motor is small, and the dynamic characteristic of the inner ring is not considered in a height channel and is described by using a second-order ARMA model.
Examples
A small quadrotor with the wheelbase of 450mm is selected, and the takeoff weight of the quadrotor is 1.2 kg.
Position control PD controller design, quad-rotor drone architecture as shown in fig. 1, its attitude angle is usually expressed using Z-Y-X euler angles, named yaw, pitch and roll, respectively. The position control of the four rotors in the Z direction uses the sum of the lift forces of the four propellers as an input, the position in the X direction uses the pitch angle as an input, and the position in the Y direction uses the roll angle as an input.
Since the attitude angle is approximately proportional to the horizontal acceleration at a small angle, the transfer function from the pitch (roll) angle to the position in the x (y) direction can be approximated as a second-order integral element. The motor lift force is in direct proportion to the vertical acceleration, so a second-order integral link can be used for representing a transfer function from the lift force to the height. Obviously, the position control transfer functions in all three directions are unstable under the open loop condition. While the minimum variance regulator requires the controlled object to be stable itself. It is first necessary to design the position closed loop so that the position control is a stable system. Here we use a PD (proportional differential) based approach to design the controller separately for three axial positions. The X-axis direction is taken as an example for explanation (the Y-axis and the Z-axis are similar).
The pitch to X-axis position transfer function is:
Figure BDA0001682317800000081
wherein g is the acceleration of gravity, theta is the pitch angle, and X is the position in the X direction.
Selecting a PD controller as follows:
Figure BDA0001682317800000082
wherein theta iscFor pitch angle command, xcFor position commands, KPAnd KDRespectively, a controller proportional parameter and a derivative parameter.
In addition, the closed loop of the pitch angle can be approximated as a link, namely:
Figure BDA0001682317800000091
the transfer function of the position closed loop thus obtained is:
Figure BDA0001682317800000092
it should be noted that the above formula is only a theoretical model, and an actual model needs to be obtained through identification.
For a selected quad-rotor platform, a minimum-variance actuator is designed here, for example, for its X-direction motion. The PD controller is first designed to make the X-direction motion closed loop stable. Selecting K through flight parameter adjustmentP＝-0.1， KD＝0.35。
Position closed loop ARMA model selection
For the convenience of implementation in a computer program, discrete models are selected for modeling the four-rotor position control axes, and in addition, the models also include descriptions about noise so as to compensate the noise in subsequent control. Here we choose the following third order ARMA model to describe the four-rotor single-axis position control:
Figure BDA0001682317800000093
wherein xc(k) At time kInputting a position instruction; x (k) is the position response output at time k; v (k) is the noise at time k; q. q.s-iDelaying by i cycles for the delay factor representation, i.e. x (k-i) ═ q-ix (k). v (k) is the variance σ2White noise sequence of (1).
It should be noted that, unlike horizontal position control, the attitude is used as the inner ring, and the height is described by using a second-order ARMA model because the motor speed command is directly used as the control input and the time constant of the motor is small, so the dynamic characteristic of the inner ring does not need to be considered in the height channel.
Position closed loop ARMA model parameter identification
The identification requires adding a pseudo-random position command sequence with proper amplitude to the aircraft with closed position loop. A4 th order M sequence (2) is selected4One cycle for 1 ═ 15 inputs) as random input x)c(k) K is 0, 1, 2., the input amplitude is selected to be 0.5m, and the period is selected to be 100 ms.
TABLE 1 pseudorandom M sequence input
Serial number 1 2 3 4 5 6 7
Input/m -0.5 0.5 0.5 0.5 -0.5 0.5 0.5
8 9 10 11 12 13 14 15
-0.5 -0.5 0.5 -0.5 0.5 -0.5 -0.5 -0.5
Through actual flight tests, a position response sequence x (k), k being 0, 1, 2.
Order to
Figure BDA0001682317800000101
According to formula (5) have
x(k)＝hT(k)θ+v(k) (7)
Further, the estimated value of the model parameter θ can be obtained by the following augmented least squares recursive algorithm
Figure BDA0001682317800000102
Figure BDA0001682317800000103
The variable k represents the kth iteration.
Figure BDA0001682317800000104
Given a set of roughly accurate values empirically, P (0) can be set to a sufficiently large unit matrix. When in use
Figure BDA0001682317800000105
And stopping iteration when the change is small along with the increase of the iteration times. Finally, a set of estimated values of the model parameters is obtained,
Figure BDA0001682317800000106
in this example, the estimated values of the model parameters are obtained as
Figure BDA0001682317800000107
Figure BDA0001682317800000108
Position closed loop minimum variance regulator design: minimum variance regulator designed according to
Figure BDA0001682317800000111
As shown in fig. 2, the minimum variance adjuster is added to the system as an outer loop of a position closed loop.
Bringing formula (9) into formula (5)
Figure BDA0001682317800000112
Bringing formula (9) and formula (10) into formula (5)
Figure BDA0001682317800000113
It can be seen that there are times when the parameter estimate is equal to the true value
x(k)＝v(k) (12)
At this time, the controlled quantity x (k) reaches a minimum variance, i.e.
E{[x(k)]2}＝σ2 (13)
Model parameters obtained by identification in 3)
Figure BDA0001682317800000114
The following minimum variance controller can be designed:
Figure BDA0001682317800000115
the method can effectively improve the position control precision of the quad-rotor unmanned aerial vehicle during suspension, and can effectively reduce the influence of system noise on the position control precision during suspension, thereby realizing high-precision position control.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description of the embodiments is for clarity only, and those skilled in the art should make the description as a whole, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (2)

1. The precise position control method of the quad-rotor unmanned aerial vehicle based on the minimum variance regulator is characterized by comprising the following steps of: the small-sized quad-rotor unmanned aerial vehicle is used as a controlled object, a position control ARMA model of the small-sized quad-rotor unmanned aerial vehicle is obtained through system identification, and a minimum variance controller is designed for the small-sized quad-rotor unmanned aerial vehicle, so that the precise hovering position control of the quad-rotor unmanned aerial vehicle is realized; an ARMA model for unmanned aerial vehicle position control is obtained through an augmented least square method, and then a minimum variance controller is designed aiming at the ARMA model, wherein the control method comprises the following steps:
step A, designing a position control PD controller, wherein the attitude angle of the PD controller is generally expressed by using a Z-Y-X Euler angle and is named as a yaw angle, a pitch angle and a roll angle respectively, the position control of the Z direction of the four rotors uses the lift sum change of four propellers as input quantity, the position of the X direction uses the pitch angle as input quantity, and the position of the Y direction uses the roll angle as input quantity; because the attitude angle and the horizontal acceleration are approximately in direct proportion under a small angle, a transfer function from the pitch angle to the position in the X direction is approximately a second-order integral link; the lift force of the motor is in direct proportion to the vertical acceleration, and a second-order integral link is used for expressing a transfer function from the lift force to the height; the position control transfer functions in three directions are unstable under the open loop condition; the minimum variance regulator requires the controlled object to be stable; therefore, firstly, a position closed loop is required to be designed to enable position control to be a stable system, and controllers are respectively designed for three axial positions by adopting a PD-based method;
the pitch to X-axis position transfer function is:
Figure FDA0001682317790000011
wherein g is the gravity acceleration, theta is the pitch angle, and X is the position in the X direction;
selecting a PD controller as follows:
Figure FDA0001682317790000012
wherein theta iscFor pitch angle command, xcFor position commands, KPAnd KDRespectively a proportional parameter and a differential parameter of the controller;
in addition, the closed loop of the pitch angle can be approximated as a link, namely:
Figure FDA0001682317790000013
the transfer function of the position closed loop thus obtained is:
Figure FDA0001682317790000014
and B, selecting a position closed loop ARMA model, wherein in order to realize a computer program, a discrete model is selected to model each axis of the four-rotor position control, in addition, the model also comprises description about noise so as to compensate the noise in subsequent control, and a third-order ARMA model is selected to describe the position control of the four rotors in a single axial direction:
Figure FDA0001682317790000025
Figure FDA0001682317790000021
wherein xc(k) Inputting a position instruction at the time k; x (k) is the position response output at time k; v (k) is the noise at time k; q. q.s-iDelaying by i cycles for the delay factor representation, i.e. x (k-i) ═ q-ix (k) v (k); is that the variance is sigma2The white noise sequence of (a);
step C, position closed loop ARIdentifying parameters of the MA model: adding a pseudo-random position instruction sequence with proper amplitude to an aircraft with a position closed loop during identification; selecting 4-order M sequence as random input xc(k) K is 0, 1, 2, the amplitude is 0.5m, and the period is 100 ms; obtaining a position response sequence x (k), k being 0, 1, 2, of the quad-rotor unmanned aerial vehicle through an actual flight test;
order to
Figure FDA0001682317790000022
According to formula (5) have
x(k)＝hT(k)θ+v(k) (7)
Further, the estimated value of the model parameter θ can be obtained by the following augmented least squares recursive algorithm
Figure FDA0001682317790000023
Figure FDA0001682317790000024
The variable k represents the kth iteration;
Figure FDA0001682317790000031
giving a group of approximately accurate values according to experience, and setting P (0) as a unit matrix large enough; when in use
Figure FDA0001682317790000032
The iteration can be stopped when the change is small along with the increase of the iteration times; finally, a set of estimated values of the model parameters is obtained,
Figure FDA0001682317790000033
step C, designing a position closed loop minimum variance regulator: minimum variance regulator designed according to
Figure FDA0001682317790000034
The minimum variance regulator is added to the system as an outer loop of the position closed loop;
bringing formula (9) into formula (5)
Figure FDA0001682317790000035
Bringing formula (9) and formula (10) into formula (5)
Figure FDA0001682317790000036
It can be seen that there are times when the parameter estimate is equal to the true value
x(k)＝v(k) (12)
At this time, the controlled quantity x (k) reaches a minimum variance, i.e.
E{[x(k)]2}＝σ2 (13) 。
2. The method of claim 1, wherein the method comprises the steps of: in the step B, the attitude is used as an inner ring for horizontal position control, the height directly uses a motor rotating speed instruction as a control input, the time constant of the motor is small, the dynamic characteristic of the inner ring is not considered in a height channel, and a second-order ARMA model is used for description.
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